Step 1: In a shallow dish or plate, combine 1/2 cup granulated sugar and 2 teaspoons ground cinnamon. Mix well and set aside for coating the churros.
Step 2: In a medium saucepan, combine the water, butter, 2 tablespoons granulated sugar, and salt. Bring to a rolling boil over medium-high heat, stirring until the butter is completely melted and sugar is dissolved.
Step 3: Remove the saucepan from the heat. Add all the all-purpose flour at once. Using a wooden spoon, stir vigorously until the mixture comes together to form a smooth ball of dough that pulls away from the sides of the pan. Continue stirring for about 30 seconds to cook out some moisture.
Step 4: Transfer the dough to a large mixing bowl (or a stand mixer fitted with a paddle attachment). Let it cool for about 5 minutes. Add the eggs one at a time, mixing well after each addition until fully incorporated and the dough is smooth, thick, and glossy.
Step 5: Fit a large star-tip nozzle (e.g., Wilton 1M or Ateco 826) onto a sturdy piping bag. Carefully spoon the churro dough into the piping bag. Do not overfill.
Step 6: In a large, deep pot or Dutch oven, heat about 2-3 inches of neutral oil (canola, vegetable, or sunflower) to 350-375°F (175-190°C). Use a candy thermometer to maintain consistent temperature.
Step 7: Carefully pipe 4-6 inch strips of dough directly into the hot oil, using kitchen shears to snip the dough from the piping bag. Fry 4-5 churros at a time to avoid overcrowding. Fry for 2-3 minutes per side, or until golden brown and cooked through.
Step 8: Using a slotted spoon or tongs, remove the fried churros from the oil and place them on a wire rack lined with paper towels to drain excess oil for a minute. Immediately transfer them to the cinnamon sugar mixture and toss to coat thoroughly.
Step 9: Repeat the frying and coating process with the remaining dough. Serve your homemade churros immediately while they are still warm and crispy, optionally with chocolate sauce or other dips.